LMFDB - Embedded newform 800.2.be.a.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(209,800)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("800.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.be (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			529.1
Character	$\chi$	$=$	800.529
Dual form			800.2.be.a.369.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.58107 - 1.87526i) q^{3} +(0.602254 + 2.15344i) q^{5} +2.97769i q^{7} +(2.21828 + 6.82716i) q^{9} +O(q^{10})$	\(q+(-2.58107 - 1.87526i) q^{3} +(0.602254 + 2.15344i) q^{5} +2.97769i q^{7} +(2.21828 + 6.82716i) q^{9} +(-0.263378 - 0.0855768i) q^{11} +(-1.36304 - 4.19500i) q^{13} +(2.48379 - 6.68755i) q^{15} +(-3.01210 - 4.14580i) q^{17} +(-0.824879 - 1.13535i) q^{19} +(5.58392 - 7.68561i) q^{21} +(0.307187 + 0.0998113i) q^{23} +(-4.27458 + 2.59383i) q^{25} +(4.11950 - 12.6785i) q^{27} +(-2.59226 + 3.56794i) q^{29} +(3.04947 - 2.21557i) q^{31} +(0.519319 + 0.714781i) q^{33} +(-6.41226 + 1.79332i) q^{35} +(-1.24835 - 3.84202i) q^{37} +(-4.34861 + 13.3836i) q^{39} +(-1.97884 - 6.09023i) q^{41} -10.9079 q^{43} +(-13.3659 + 8.88860i) q^{45} +(-1.67150 + 2.30062i) q^{47} -1.86662 q^{49} +16.3491i q^{51} +(-0.378304 - 0.274854i) q^{53} +(0.0256637 - 0.618708i) q^{55} +4.47727i q^{57} +(-5.09147 + 1.65432i) q^{59} +(1.96419 + 0.638204i) q^{61} +(-20.3291 + 6.60534i) q^{63} +(8.21278 - 5.46168i) q^{65} +(1.25093 - 0.908853i) q^{67} +(-0.605700 - 0.833675i) q^{69} +(-7.81261 - 5.67620i) q^{71} +(-8.54291 - 2.77576i) q^{73} +(15.8971 + 1.32108i) q^{75} +(0.254821 - 0.784258i) q^{77} +(-4.49455 - 3.26548i) q^{79} +(-16.9856 + 12.3407i) q^{81} +(10.7440 - 7.80599i) q^{83} +(7.11368 - 8.98320i) q^{85} +(13.3816 - 4.34795i) q^{87} +(0.992059 - 3.05324i) q^{89} +(12.4914 - 4.05871i) q^{91} -12.0257 q^{93} +(1.94811 - 2.46009i) q^{95} +(9.69449 - 13.3433i) q^{97} -1.98796i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 30 q^{9}+O(q^{10}) $ 112 * q - 30 * q^9	$ 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79} - 6 q^{81} + 10 q^{87} + 24 q^{89} + 86 q^{95} - 50 q^{97}+O(q^{100}) $ 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.58107	−	1.87526i	−1.49018	−	1.08268i	−0.974094	−	0.226143i	$-0.927388\pi$
$3$	−2.58107	−	1.87526i	−1.49018	−	1.08268i	−0.516086	−	0.856537i	$-0.672612\pi$
$4$		0			0
$5$	0.602254	+	2.15344i	0.269336	+	0.963046i
$5$	0.602254	+	2.15344i	0.269336	+	0.963046i
$6$		0			0
$7$			2.97769i			1.12546i	0.826641	+	0.562730i	$0.190249\pi$
$7$			2.97769i			1.12546i	−0.826641	+	0.562730i	$0.809751\pi$
$8$		0			0
$9$	2.21828	+	6.82716i	0.739426	+	2.27572i
$10$		0			0
$11$	−0.263378	−	0.0855768i	−0.0794116	−	0.0258024i	0.269042	−	0.963129i	$-0.413293\pi$
$11$	−0.263378	−	0.0855768i	−0.0794116	−	0.0258024i	−0.348453	+	0.937326i	$0.613293\pi$
$12$		0			0
$13$	−1.36304	−	4.19500i	−0.378039	−	1.16349i	−0.941405	−	0.337278i	$-0.890494\pi$
$13$	−1.36304	−	4.19500i	−0.378039	−	1.16349i	0.563366	−	0.826207i	$-0.309506\pi$
$14$		0			0
$15$	2.48379	−	6.68755i	0.641311	−	1.72672i
$16$		0			0
$17$	−3.01210	−	4.14580i	−0.730542	−	1.00551i	−0.999107	−	0.0422436i	$-0.986549\pi$
$17$	−3.01210	−	4.14580i	−0.730542	−	1.00551i	0.268565	−	0.963262i	$-0.413451\pi$
$18$		0			0
$19$	−0.824879	−	1.13535i	−0.189240	−	0.260467i	0.703846	−	0.710353i	$-0.251465\pi$
$19$	−0.824879	−	1.13535i	−0.189240	−	0.260467i	−0.893086	+	0.449886i	$0.851465\pi$
$20$		0			0
$21$	5.58392	−	7.68561i	1.21851	−	1.67714i
$22$		0			0
$23$	0.307187	+	0.0998113i	0.0640530	+	0.0208121i	0.340868	−	0.940111i	$-0.389279\pi$
$23$	0.307187	+	0.0998113i	0.0640530	+	0.0208121i	−0.276815	+	0.960923i	$0.589279\pi$
$24$		0			0
$25$	−4.27458	+	2.59383i	−0.854916	+	0.518766i
$26$		0			0
$27$	4.11950	−	12.6785i	0.792798	−	2.43998i
$28$		0			0
$29$	−2.59226	+	3.56794i	−0.481371	+	0.662550i	−0.978768	−	0.204973i	$-0.934289\pi$
$29$	−2.59226	+	3.56794i	−0.481371	+	0.662550i	0.497397	+	0.867523i	$0.334289\pi$
$30$		0			0
$31$	3.04947	−	2.21557i	0.547702	−	0.397929i	−0.279236	−	0.960223i	$-0.590081\pi$
$31$	3.04947	−	2.21557i	0.547702	−	0.397929i	0.826937	+	0.562294i	$0.190081\pi$
$32$		0			0
$33$	0.519319	+	0.714781i	0.0904018	+	0.124427i
$34$		0			0
$35$	−6.41226	+	1.79332i	−1.08387	+	0.303127i
$36$		0			0
$37$	−1.24835	−	3.84202i	−0.205227	−	0.631625i	−0.999704	−	0.0243301i	$-0.992255\pi$
$37$	−1.24835	−	3.84202i	−0.205227	−	0.631625i	0.794477	−	0.607295i	$-0.207745\pi$
$38$		0			0
$39$	−4.34861	+	13.3836i	−0.696335	+	2.14310i
$40$		0			0
$41$	−1.97884	−	6.09023i	−0.309042	−	0.951135i	−0.978138	−	0.207958i	$-0.933318\pi$
$41$	−1.97884	−	6.09023i	−0.309042	−	0.951135i	0.669095	−	0.743177i	$-0.266682\pi$
$42$		0			0
$43$	−10.9079			−1.66343			−0.831717	−	0.555199i	$-0.812642\pi$
$43$	−10.9079			−1.66343			−0.831717	+	0.555199i	$0.812642\pi$
$44$		0			0
$45$	−13.3659	+	8.88860i	−1.99247	+	1.32503i
$46$		0			0
$47$	−1.67150	+	2.30062i	−0.243813	+	0.335580i	−0.913333	−	0.407214i	$-0.866500\pi$
$47$	−1.67150	+	2.30062i	−0.243813	+	0.335580i	0.669519	+	0.742795i	$0.266500\pi$
$48$		0			0
$49$	−1.86662			−0.266660
$50$		0			0
$51$			16.3491i			2.28933i
$52$		0			0
$53$	−0.378304	−	0.274854i	−0.0519641	−	0.0377541i	0.561500	−	0.827477i	$-0.310224\pi$
$53$	−0.378304	−	0.274854i	−0.0519641	−	0.0377541i	−0.613464	+	0.789723i	$0.710224\pi$
$54$		0			0
$55$	0.0256637	−	0.618708i	0.00346050	−	0.0834265i
$56$		0			0
$57$			4.47727i			0.593029i
$58$		0			0
$59$	−5.09147	+	1.65432i	−0.662853	+	0.215374i	−0.621073	−	0.783753i	$-0.713303\pi$
$59$	−5.09147	+	1.65432i	−0.662853	+	0.215374i	−0.0417804	+	0.999127i	$0.513303\pi$
$60$		0			0
$61$	1.96419	+	0.638204i	0.251489	+	0.0817137i	0.432049	−	0.901850i	$-0.357791\pi$
$61$	1.96419	+	0.638204i	0.251489	+	0.0817137i	−0.180560	+	0.983564i	$0.557791\pi$
$62$		0			0
$63$	−20.3291	+	6.60534i	−2.56123	+	0.832194i
$64$		0			0
$65$	8.21278	−	5.46168i	1.01867	−	0.677438i
$66$		0			0
$67$	1.25093	−	0.908853i	0.152825	−	0.111034i	−0.508745	−	0.860917i	$-0.669890\pi$
$67$	1.25093	−	0.908853i	0.152825	−	0.111034i	0.661570	+	0.749883i	$0.269890\pi$
$68$		0			0
$69$	−0.605700	−	0.833675i	−0.0729177	−	0.100363i
$70$		0			0
$71$	−7.81261	−	5.67620i	−0.927187	−	0.673640i	0.0181158	−	0.999836i	$-0.494233\pi$
$71$	−7.81261	−	5.67620i	−0.927187	−	0.673640i	−0.945302	+	0.326195i	$0.894233\pi$
$72$		0			0
$73$	−8.54291	−	2.77576i	−0.999872	−	0.324878i	−0.237057	−	0.971496i	$-0.576183\pi$
$73$	−8.54291	−	2.77576i	−0.999872	−	0.324878i	−0.762814	+	0.646618i	$0.776183\pi$
$74$		0			0
$75$	15.8971	+	1.32108i	1.83564	+	0.152545i
$76$		0			0
$77$	0.254821	−	0.784258i	0.0290395	−	0.0893745i
$78$		0			0
$79$	−4.49455	−	3.26548i	−0.505677	−	0.367396i	0.305504	−	0.952191i	$-0.401175\pi$
$79$	−4.49455	−	3.26548i	−0.505677	−	0.367396i	−0.811181	+	0.584795i	$0.801175\pi$
$80$		0			0
$81$	−16.9856	+	12.3407i	−1.88729	+	1.37119i
$82$		0			0
$83$	10.7440	−	7.80599i	1.17931	−	0.856819i	0.187217	−	0.982319i	$-0.440053\pi$
$83$	10.7440	−	7.80599i	1.17931	−	0.856819i	0.992094	+	0.125500i	$0.0400534\pi$
$84$		0			0
$85$	7.11368	−	8.98320i	0.771587	−	0.974365i
$86$		0			0
$87$	13.3816	−	4.34795i	1.43466	−	0.466149i
$88$		0			0
$89$	0.992059	−	3.05324i	0.105158	−	0.323643i	−0.884610	−	0.466333i	$-0.845575\pi$
$89$	0.992059	−	3.05324i	0.105158	−	0.323643i	0.989768	+	0.142689i	$0.0455750\pi$
$90$		0			0
$91$	12.4914	−	4.05871i	1.30946	−	0.425468i
$92$		0			0
$93$	−12.0257			−1.24700
$94$		0			0
$95$	1.94811	−	2.46009i	0.199872	−	0.252400i
$96$		0			0
$97$	9.69449	−	13.3433i	0.984327	−	1.35481i	0.0498611	−	0.998756i	$-0.484122\pi$
$97$	9.69449	−	13.3433i	0.984327	−	1.35481i	0.934466	−	0.356053i	$-0.115878\pi$
$98$		0			0
$99$		−	1.98796i		−	0.199797i
$100$		0			0
$101$			19.4874i			1.93907i	0.244946	+	0.969537i	$0.421230\pi$
$101$			19.4874i			1.93907i	−0.244946	+	0.969537i	$0.578770\pi$
$102$		0			0
$103$	4.15447	−	5.71814i	0.409352	−	0.563425i	−0.553708	−	0.832711i	$-0.686788\pi$
$103$	4.15447	−	5.71814i	0.409352	−	0.563425i	0.963060	+	0.269286i	$0.0867877\pi$
$104$		0			0
$105$	19.9134	+	7.39594i	1.94335	+	0.721770i
$106$		0			0
$107$	−11.2557			−1.08813			−0.544064	−	0.839044i	$-0.683115\pi$
$107$	−11.2557			−1.08813			−0.544064	+	0.839044i	$0.683115\pi$
$108$		0			0
$109$	−9.07913	+	2.94999i	−0.869623	+	0.282558i	−0.709642	−	0.704563i	$-0.751143\pi$
$109$	−9.07913	+	2.94999i	−0.869623	+	0.282558i	−0.159981	+	0.987120i	$0.551143\pi$
$110$		0			0
$111$	−3.98270	+	12.2575i	−0.378021	+	1.16343i
$112$		0			0
$113$	−10.0510	+	3.26576i	−0.945517	+	0.307217i	−0.740892	−	0.671624i	$-0.765597\pi$
$113$	−10.0510	+	3.26576i	−0.945517	+	0.307217i	−0.204624	+	0.978841i	$0.565597\pi$
$114$		0			0
$115$	−0.0299325	+	0.721621i	−0.00279122	+	0.0672915i
$116$		0			0
$117$	25.6164	−	18.6114i	2.36823	−	1.72062i
$118$		0			0
$119$	12.3449	−	8.96910i	1.13166	−	0.822196i
$120$		0			0
$121$	−8.83714	−	6.42056i	−0.803377	−	0.583687i
$122$		0			0
$123$	−6.31323	+	19.4301i	−0.569245	+	1.75196i
$124$		0			0
$125$	−8.16003	−	7.64290i	−0.729855	−	0.683602i
$126$		0			0
$127$	−1.29082	−	0.419412i	−0.114542	−	0.0372168i	0.251185	−	0.967939i	$-0.419180\pi$
$127$	−1.29082	−	0.419412i	−0.114542	−	0.0372168i	−0.365727	+	0.930722i	$0.619180\pi$
$128$		0			0
$129$	28.1540	+	20.4550i	2.47882	+	1.80097i
$130$		0			0
$131$	−0.471129	−	0.648453i	−0.0411627	−	0.0566556i	0.787940	−	0.615753i	$-0.211148\pi$
$131$	−0.471129	−	0.648453i	−0.0411627	−	0.0566556i	−0.829102	+	0.559097i	$0.811148\pi$
$132$		0			0
$133$	3.38071	−	2.45623i	0.293145	−	0.212982i
$134$		0			0
$135$	29.7834	+	1.23540i	2.56334	+	0.106326i
$136$		0			0
$137$	−6.89354	+	2.23985i	−0.588955	+	0.191363i	−0.588308	−	0.808637i	$-0.700206\pi$
$137$	−6.89354	+	2.23985i	−0.588955	+	0.191363i	−0.000646705		1.00000i	$0.500206\pi$
$138$		0			0
$139$	0.417329	+	0.135598i	0.0353973	+	0.0115013i	0.326662	−	0.945141i	$-0.394076\pi$
$139$	0.417329	+	0.135598i	0.0353973	+	0.0115013i	−0.291265	+	0.956642i	$0.594076\pi$
$140$		0			0
$141$	8.62851	−	2.80357i	0.726652	−	0.236103i
$142$		0			0
$143$			1.22152i			0.102148i
$144$		0			0
$145$	−9.24453	−	3.43346i	−0.767717	−	0.285134i
$146$		0			0
$147$	4.81787	+	3.50039i	0.397372	+	0.288707i
$148$		0			0
$149$			1.65547i			0.135621i	0.997698	+	0.0678107i	$0.0216014\pi$
$149$			1.65547i			0.135621i	−0.997698	+	0.0678107i	$0.978399\pi$
$150$		0			0
$151$	14.0629			1.14442			0.572211	−	0.820107i	$-0.306086\pi$
$151$	14.0629			1.14442			0.572211	+	0.820107i	$0.306086\pi$
$152$		0			0
$153$	21.6224	−	29.7606i	1.74806	−	2.40600i
$154$		0			0
$155$	6.60765	+	5.23251i	0.530739	+	0.420286i
$156$		0			0
$157$	−9.56521			−0.763387			−0.381693	−	0.924289i	$-0.624659\pi$
$157$	−9.56521			−0.763387			−0.381693	+	0.924289i	$0.624659\pi$
$158$		0			0
$159$	0.461007	+	1.41883i	0.0365603	+	0.112521i
$160$		0			0
$161$	−0.297207	+	0.914708i	−0.0234232	+	0.0720891i
$162$		0			0
$163$	−1.69722	−	5.22350i	−0.132936	−	0.409136i	0.862327	−	0.506352i	$-0.169006\pi$
$163$	−1.69722	−	5.22350i	−0.132936	−	0.409136i	−0.995263	+	0.0972156i	$0.969006\pi$
$164$		0			0
$165$	−1.22647	+	1.54880i	−0.0954809	+	0.120574i
$166$		0			0
$167$	7.07399	+	9.73651i	0.547401	+	0.753433i	0.989657	−	0.143456i	$-0.0458215\pi$
$167$	7.07399	+	9.73651i	0.547401	+	0.753433i	−0.442255	+	0.896889i	$0.645821\pi$
$168$		0			0
$169$	−5.22297	+	3.79471i	−0.401767	+	0.291901i
$170$		0			0
$171$	5.92139	−	8.15009i	0.452820	−	0.623253i
$172$		0			0
$173$	−5.37296	+	16.5363i	−0.408498	+	1.25723i	0.509440	+	0.860506i	$0.329852\pi$
$173$	−5.37296	+	16.5363i	−0.408498	+	1.25723i	−0.917939	+	0.396722i	$0.870148\pi$
$174$		0			0
$175$	−7.72361	−	12.7284i	−0.583850	−	0.962174i
$176$		0			0
$177$	16.2437	+	5.27790i	1.22095	+	0.396711i
$178$		0			0
$179$	12.5073	−	17.2148i	0.934841	−	1.28670i	−0.0231007	−	0.999733i	$-0.507354\pi$
$179$	12.5073	−	17.2148i	0.934841	−	1.28670i	0.957941	−	0.286964i	$-0.0926462\pi$
$180$		0			0
$181$	4.82937	+	6.64706i	0.358964	+	0.494072i	0.949860	−	0.312676i	$-0.101225\pi$
$181$	4.82937	+	6.64706i	0.358964	+	0.494072i	−0.590896	+	0.806748i	$0.701225\pi$
$182$		0			0
$183$	−3.87291	−	5.33061i	−0.286294	−	0.394050i
$184$		0			0
$185$	7.52173	−	5.00211i	0.553009	−	0.367763i
$186$		0			0
$187$	0.438538	+	1.34968i	0.0320691	+	0.0986985i
$188$		0			0
$189$	37.7526	+	12.2666i	2.74610	+	0.892262i
$190$		0			0
$191$	1.09517	+	3.37058i	0.0792436	+	0.243887i	0.982828	−	0.184523i	$-0.0590740\pi$
$191$	1.09517	+	3.37058i	0.0792436	+	0.243887i	−0.903585	+	0.428410i	$0.859074\pi$
$192$		0			0
$193$		−	13.3961i		−	0.964273i	−0.876096	−	0.482137i	$-0.839861\pi$
$193$		−	13.3961i		−	0.964273i	0.876096	−	0.482137i	$-0.160139\pi$
$194$		0			0
$195$	−31.4398	−	1.30411i	−2.25145	−	0.0933892i
$196$		0			0
$197$	−4.15379	−	3.01790i	−0.295945	−	0.215017i	0.429897	−	0.902878i	$-0.358550\pi$
$197$	−4.15379	−	3.01790i	−0.295945	−	0.215017i	−0.725842	+	0.687861i	$0.758550\pi$
$198$		0			0
$199$	−12.5552			−0.890012			−0.445006	−	0.895528i	$-0.646798\pi$
$199$	−12.5552			−0.890012			−0.445006	+	0.895528i	$0.646798\pi$
$200$		0			0
$201$	−4.93307			−0.347952
$202$		0			0
$203$	−10.6242	−	7.71894i	−0.745673	−	0.541763i
$204$		0			0
$205$	11.9232	−	7.92916i	0.832750	−	0.553797i
$206$		0			0
$207$			2.31863i			0.161156i
$208$		0			0
$209$	0.120096	+	0.369617i	0.00830719	+	0.0255669i
$210$		0			0
$211$	7.25107	+	2.35602i	0.499184	+	0.162195i	0.547778	−	0.836624i	$-0.315474\pi$
$211$	7.25107	+	2.35602i	0.499184	+	0.162195i	−0.0485936	+	0.998819i	$0.515474\pi$
$212$		0			0
$213$	9.52057	+	29.3013i	0.652339	+	2.00769i
$214$		0			0
$215$	−6.56930	−	23.4894i	−0.448023	−	1.60196i
$216$		0			0
$217$	6.59728	+	9.08038i	0.447853	+	0.616416i
$218$		0			0
$219$	16.8446	+	23.1846i	1.13825	+	1.56667i
$220$		0			0
$221$	−13.2861	+	18.2867i	−0.893717	+	1.23010i
$222$		0			0
$223$	−18.3487	−	5.96185i	−1.22872	−	0.399235i	−0.378469	−	0.925614i	$-0.623549\pi$
$223$	−18.3487	−	5.96185i	−1.22872	−	0.399235i	−0.850250	+	0.526379i	$0.823549\pi$
$224$		0			0
$225$	−27.1907	−	23.4294i	−1.81271	−	1.56196i
$226$		0			0
$227$	−7.44462	+	22.9122i	−0.494117	+	1.52073i	0.324212	+	0.945984i	$0.394901\pi$
$227$	−7.44462	+	22.9122i	−0.494117	+	1.52073i	−0.818329	+	0.574751i	$0.805099\pi$
$228$		0			0
$229$	15.5176	−	21.3582i	1.02544	−	1.41139i	0.117113	−	0.993119i	$-0.462636\pi$
$229$	15.5176	−	21.3582i	1.02544	−	1.41139i	0.908322	−	0.418272i	$-0.137364\pi$
$230$		0			0
$231$	−2.12840	+	1.54637i	−0.140038	+	0.101744i
$232$		0			0
$233$	14.2161	+	19.5668i	0.931328	+	1.28186i	0.959339	+	0.282256i	$0.0910827\pi$
$233$	14.2161	+	19.5668i	0.931328	+	1.28186i	−0.0280108	+	0.999608i	$0.508917\pi$
$234$		0			0
$235$	−5.96091	−	2.21391i	−0.388847	−	0.144420i
$236$		0			0
$237$	5.47713	+	16.8569i	0.355778	+	1.09497i
$238$		0			0
$239$	−4.76280	+	14.6584i	−0.308080	+	0.948173i	0.670430	+	0.741973i	$0.266110\pi$
$239$	−4.76280	+	14.6584i	−0.308080	+	0.948173i	−0.978510	+	0.206200i	$0.933890\pi$
$240$		0			0
$241$	4.82186	+	14.8402i	0.310604	+	0.955940i	0.977526	+	0.210813i	$0.0676111\pi$
$241$	4.82186	+	14.8402i	0.310604	+	0.955940i	−0.666923	+	0.745127i	$0.732389\pi$
$242$		0			0
$243$	26.9901			1.73141
$244$		0			0
$245$	−1.12418	−	4.01965i	−0.0718211	−	0.256806i
$246$		0			0
$247$	−3.63845	+	5.00790i	−0.231509	+	0.318645i
$248$		0			0
$249$	−42.3693			−2.68505
$250$		0			0
$251$		−	2.59224i		−	0.163621i	−0.996648	−	0.0818104i	$-0.973930\pi$
$251$		−	2.59224i		−	0.163621i	0.996648	−	0.0818104i	$-0.0260702\pi$
$252$		0			0
$253$	−0.0723650	−	0.0525763i	−0.00454955	−	0.00330544i
$254$		0			0
$255$	−35.2067	+	9.84628i	−2.20473	+	0.616598i
$256$		0			0
$257$			1.98944i			0.124098i	0.998073	+	0.0620490i	$0.0197635\pi$
$257$			1.98944i			0.124098i	−0.998073	+	0.0620490i	$0.980236\pi$
$258$		0			0
$259$	11.4403	−	3.71719i	0.710868	−	0.230975i
$260$		0			0
$261$	−30.1092	−	9.78308i	−1.86371	−	0.605558i
$262$		0			0
$263$	14.8066	−	4.81097i	0.913017	−	0.296657i	0.185418	−	0.982660i	$-0.440636\pi$
$263$	14.8066	−	4.81097i	0.913017	−	0.296657i	0.727599	+	0.686003i	$0.240636\pi$
$264$		0			0
$265$	0.364046	−	0.980187i	0.0223632	−	0.0602124i
$266$		0			0
$267$	−8.28618	+	6.02026i	−0.507106	+	0.368434i
$268$		0			0
$269$	−0.776787	−	1.06916i	−0.0473616	−	0.0651876i	0.784679	−	0.619902i	$-0.212828\pi$
$269$	−0.776787	−	1.06916i	−0.0473616	−	0.0651876i	−0.832041	+	0.554714i	$0.812828\pi$
$270$		0			0
$271$	−11.7169	−	8.51285i	−0.711753	−	0.517119i	0.171986	−	0.985099i	$-0.444982\pi$
$271$	−11.7169	−	8.51285i	−0.711753	−	0.517119i	−0.883739	+	0.467981i	$0.844982\pi$
$272$		0			0
$273$	−39.8523	−	12.9488i	−2.41197	−	0.783697i
$274$		0			0
$275$	1.34780	−	0.317354i	0.0812756	−	0.0191371i
$276$		0			0
$277$	−3.95585	+	12.1748i	−0.237684	+	0.731516i	0.759070	+	0.651009i	$0.225654\pi$
$277$	−3.95585	+	12.1748i	−0.237684	+	0.731516i	−0.996754	+	0.0805069i	$0.974346\pi$
$278$		0			0
$279$	21.8906	+	15.9045i	1.31056	+	0.952176i
$280$		0			0
$281$	−2.54841	+	1.85153i	−0.152025	+	0.110453i	−0.661198	−	0.750212i	$-0.729952\pi$
$281$	−2.54841	+	1.85153i	−0.152025	+	0.110453i	0.509172	+	0.860665i	$0.329952\pi$
$282$		0			0
$283$	−10.1940	+	7.40638i	−0.605971	+	0.440264i	−0.847993	−	0.530007i	$-0.822189\pi$
$283$	−10.1940	+	7.40638i	−0.605971	+	0.440264i	0.242022	+	0.970271i	$0.422189\pi$
$284$		0			0
$285$	−9.64152	+	2.69645i	−0.571114	+	0.159724i
$286$		0			0
$287$	18.1348	−	5.89236i	1.07046	−	0.347815i
$288$		0			0
$289$	−2.86164	+	8.80721i	−0.168332	+	0.518071i
$290$		0			0
$291$	−50.0443	+	16.2604i	−2.93365	+	0.953200i
$292$		0			0
$293$	9.19701			0.537295			0.268647	−	0.963239i	$-0.413423\pi$
$293$	9.19701			0.537295			0.268647	+	0.963239i	$0.413423\pi$
$294$		0			0
$295$	−6.62883	−	9.96785i	−0.385946	−	0.580351i
$296$		0			0
$297$	−2.16997	+	2.98671i	−0.125915	+	0.173307i
$298$		0			0
$299$		−	1.42470i		−	0.0823925i
$300$		0			0
$301$		−	32.4802i		−	1.87213i
$302$		0			0
$303$	36.5440	−	50.2984i	2.09940	−	2.88957i
$304$		0			0
$305$	−0.191392	+	4.61412i	−0.0109591	+	0.264204i
$306$		0			0
$307$	24.3699			1.39087			0.695433	−	0.718591i	$-0.255213\pi$
$307$	24.3699			1.39087			0.695433	+	0.718591i	$0.255213\pi$
$308$		0			0
$309$	−21.4459	+	6.96821i	−1.22002	+	0.396407i
$310$		0			0
$311$	−7.74867	+	23.8479i	−0.439387	+	1.35229i	0.449138	+	0.893463i	$0.351731\pi$
$311$	−7.74867	+	23.8479i	−0.439387	+	1.35229i	−0.888524	+	0.458830i	$0.848269\pi$
$312$		0			0
$313$	10.3764	−	3.37148i	0.586506	−	0.190567i	−0.000706882	−	1.00000i	$-0.500225\pi$
$313$	10.3764	−	3.37148i	0.586506	−	0.190567i	0.587213	+	0.809432i	$0.300225\pi$
$314$		0			0
$315$	−26.4675	−	39.7994i	−1.49127	−	2.24244i
$316$		0			0
$317$	0.695505	−	0.505314i	0.0390635	−	0.0283813i	−0.568082	−	0.822972i	$-0.692314\pi$
$317$	0.695505	−	0.505314i	0.0390635	−	0.0283813i	0.607146	+	0.794591i	$0.292314\pi$
$318$		0			0
$319$	0.988078	−	0.717881i	0.0553218	−	0.0401936i
$320$		0			0
$321$	29.0517	+	21.1073i	1.62151	+	1.17809i
$322$		0			0
$323$	−2.22231	+	6.83957i	−0.123653	+	0.380564i
$324$		0			0
$325$	16.7076	+	14.3964i	0.926768	+	0.798568i
$326$		0			0
$327$	28.9658	+	9.41157i	1.60181	+	0.520461i
$328$		0			0
$329$	−6.85053	−	4.97720i	−0.377682	−	0.274402i
$330$		0			0
$331$	−4.98309	−	6.85864i	−0.273895	−	0.376985i	0.649805	−	0.760101i	$-0.274851\pi$
$331$	−4.98309	−	6.85864i	−0.273895	−	0.376985i	−0.923700	+	0.383117i	$0.874851\pi$
$332$		0			0
$333$	23.4609	−	17.0453i	1.28565	−	0.934079i
$334$		0			0
$335$	2.71053	+	2.14644i	0.148092	+	0.117272i
$336$		0			0
$337$	15.9864	−	5.19430i	0.870835	−	0.282951i	0.160688	−	0.987005i	$-0.448629\pi$
$337$	15.9864	−	5.19430i	0.870835	−	0.282951i	0.710147	+	0.704054i	$0.248629\pi$
$338$		0			0
$339$	32.0664	+	10.4190i	1.74161	+	0.565883i
$340$		0			0
$341$	−0.992767	+	0.322570i	−0.0537613	+	0.0174681i
$342$		0			0
$343$			15.2856i			0.825345i
$344$		0			0
$345$	1.43048	−	1.80642i	0.0770145	−	0.0972544i
$346$		0			0
$347$	14.2663	+	10.3651i	0.765856	+	0.556427i	0.900701	−	0.434440i	$-0.143054\pi$
$347$	14.2663	+	10.3651i	0.765856	+	0.556427i	−0.134845	+	0.990867i	$0.543054\pi$
$348$		0			0
$349$		−	35.1956i		−	1.88398i	−0.335642	−	0.941990i	$-0.608953\pi$
$349$		−	35.1956i		−	1.88398i	0.335642	−	0.941990i	$-0.391047\pi$
$350$		0			0
$351$	−58.8015			−3.13859
$352$		0			0
$353$	−16.7024	+	22.9889i	−0.888980	+	1.22358i	0.0848720	+	0.996392i	$0.472952\pi$
$353$	−16.7024	+	22.9889i	−0.888980	+	1.22358i	−0.973852	+	0.227184i	$0.927048\pi$
$354$		0			0
$355$	7.51815	−	20.2425i	0.399022	−	1.07436i
$356$		0			0
$357$	−48.6824			−2.57655
$358$		0			0
$359$	−3.94315	−	12.1358i	−0.208112	−	0.640501i	−0.999571	−	0.0292801i	$-0.990679\pi$
$359$	−3.94315	−	12.1358i	−0.208112	−	0.640501i	0.791460	−	0.611221i	$-0.209321\pi$
$360$		0			0
$361$	5.26273	−	16.1970i	0.276986	−	0.852475i
$362$		0			0
$363$	10.7691	+	33.1438i	0.565230	+	1.73960i
$364$		0			0
$365$	0.832425	−	20.0683i	0.0435711	−	1.05042i
$366$		0			0
$367$	−12.5338	−	17.2512i	−0.654257	−	0.900507i	0.345018	−	0.938596i	$-0.387873\pi$
$367$	−12.5338	−	17.2512i	−0.654257	−	0.900507i	−0.999274	+	0.0380891i	$0.987873\pi$
$368$		0			0
$369$	37.1894	−	27.0197i	1.93600	−	1.40659i
$370$		0			0
$371$	0.818430	−	1.12647i	0.0424908	−	0.0584835i
$372$		0			0
$373$	−3.63793	+	11.1964i	−0.188365	+	0.579727i	−0.999990	−	0.00445132i	$-0.998583\pi$
$373$	−3.63793	+	11.1964i	−0.188365	+	0.579727i	0.811625	+	0.584178i	$0.198583\pi$
$374$		0			0
$375$	6.72921	+	35.0290i	0.347495	+	1.80889i
$376$		0			0
$377$	18.5009	+	6.01130i	0.952844	+	0.309598i
$378$		0			0
$379$	10.7274	−	14.7650i	0.551030	−	0.758428i	−0.439121	−	0.898428i	$-0.644710\pi$
$379$	10.7274	−	14.7650i	0.551030	−	0.758428i	0.990152	+	0.140000i	$0.0447102\pi$
$380$		0			0
$381$	2.54518	+	3.50315i	0.130394	+	0.179472i
$382$		0			0
$383$	21.1437	+	29.1018i	1.08039	+	1.48703i	0.859087	+	0.511830i	$0.171032\pi$
$383$	21.1437	+	29.1018i	1.08039	+	1.48703i	0.221307	+	0.975204i	$0.428968\pi$
$384$		0			0
$385$	1.84232	+	0.0764185i	0.0938932	+	0.00389465i
$386$		0			0
$387$	−24.1967	−	74.4697i	−1.22999	−	3.78551i
$388$		0			0
$389$	−2.67533	−	0.869269i	−0.135645	−	0.0440737i	0.240408	−	0.970672i	$-0.422719\pi$
$389$	−2.67533	−	0.869269i	−0.135645	−	0.0440737i	−0.376053	+	0.926598i	$0.622719\pi$
$390$		0			0
$391$	−0.511482	−	1.57418i	−0.0258668	−	0.0796097i
$392$		0			0
$393$			2.55719i			0.128993i
$394$		0			0
$395$	4.32515	−	11.6454i	0.217622	−	0.585943i
$396$		0			0
$397$	−6.36873	−	4.62715i	−0.319637	−	0.232230i	0.416383	−	0.909189i	$-0.363297\pi$
$397$	−6.36873	−	4.62715i	−0.319637	−	0.232230i	−0.736021	+	0.676959i	$0.763297\pi$
$398$		0			0
$399$	−13.3319			−0.667430
$400$		0			0
$401$	−6.74733			−0.336946			−0.168473	−	0.985706i	$-0.553884\pi$
$401$	−6.74733			−0.336946			−0.168473	+	0.985706i	$0.553884\pi$
$402$		0			0
$403$	−13.4509	−	9.77264i	−0.670037	−	0.486810i
$404$		0			0
$405$	−36.8046	−	29.1451i	−1.82884	−	1.44823i
$406$		0			0
$407$			1.11874i			0.0554537i
$408$		0			0
$409$	−8.52623	−	26.2411i	−0.421595	−	1.29754i	−0.906217	−	0.422813i	$-0.861043\pi$
$409$	−8.52623	−	26.2411i	−0.421595	−	1.29754i	0.484622	−	0.874724i	$-0.338957\pi$
$410$		0			0
$411$	21.9930	+	7.14596i	1.08483	+	0.352484i
$412$		0			0
$413$	−4.92605	−	15.1608i	−0.242395	−	0.746015i
$414$		0			0
$415$	23.2803	+	18.4354i	1.14279	+	0.904958i
$416$		0			0
$417$	−0.822872	−	1.13259i	−0.0402962	−	0.0554630i
$418$		0			0
$419$	−14.4072	−	19.8299i	−0.703839	−	0.968752i	−0.999908	−	0.0135851i	$-0.995676\pi$
$419$	−14.4072	−	19.8299i	−0.703839	−	0.968752i	0.296068	−	0.955167i	$-0.404324\pi$
$420$		0			0
$421$	−15.9444	+	21.9456i	−0.777084	+	1.06956i	0.218514	+	0.975834i	$0.429879\pi$
$421$	−15.9444	+	21.9456i	−0.777084	+	1.06956i	−0.995598	+	0.0937303i	$0.970121\pi$
$422$		0			0
$423$	−19.4146	−	6.30817i	−0.943968	−	0.306714i
$424$		0			0
$425$	23.6290	+	9.90869i	1.14617	+	0.480642i
$426$		0			0
$427$	−1.90037	+	5.84875i	−0.0919655	+	0.283041i
$428$		0			0
$429$	2.29066	−	3.15282i	0.110594	−	0.152220i
$430$		0			0
$431$	6.94699	−	5.04728i	0.334625	−	0.243119i	−0.407766	−	0.913087i	$-0.633692\pi$
$431$	6.94699	−	5.04728i	0.334625	−	0.243119i	0.742390	+	0.669968i	$0.233692\pi$
$432$		0			0
$433$	17.2045	+	23.6800i	0.826797	+	1.13799i	0.988511	+	0.151150i	$0.0482978\pi$
$433$	17.2045	+	23.6800i	0.826797	+	1.13799i	−0.161714	+	0.986838i	$0.551702\pi$
$434$		0			0
$435$	17.4221	+	26.1979i	0.835328	+	1.25609i
$436$		0			0
$437$	−0.140072	−	0.431097i	−0.00670055	−	0.0206222i
$438$		0			0
$439$	−3.98757	+	12.2725i	−0.190317	+	0.585734i	−0.999999	−	0.00113362i	$-0.999639\pi$
$439$	−3.98757	+	12.2725i	−0.190317	+	0.585734i	0.809683	+	0.586868i	$0.199639\pi$
$440$		0			0
$441$	−4.14068	−	12.7437i	−0.197175	−	0.606843i
$442$		0			0
$443$	1.10768			0.0526274			0.0263137	−	0.999654i	$-0.491623\pi$
$443$	1.10768			0.0526274			0.0263137	+	0.999654i	$0.491623\pi$
$444$		0			0
$445$	7.17244	+	0.297510i	0.340006	+	0.0141033i
$446$		0			0
$447$	3.10443	−	4.27288i	0.146834	−	0.202100i
$448$		0			0
$449$	−6.01273			−0.283758			−0.141879	−	0.989884i	$-0.545314\pi$
$449$	−6.01273			−0.283758			−0.141879	+	0.989884i	$0.545314\pi$
$450$		0			0
$451$			1.77338i			0.0835051i
$452$		0			0
$453$	−36.2973	−	26.3715i	−1.70539	−	1.23904i
$454$		0			0
$455$	16.2632	+	24.4551i	0.762429	+	1.14647i
$456$		0			0
$457$			36.8695i			1.72468i	0.506328	+	0.862341i	$0.331003\pi$
$457$			36.8695i			1.72468i	−0.506328	+	0.862341i	$0.668997\pi$
$458$		0			0
$459$	−64.9710	+	21.1103i	−3.03258	+	0.985347i
$460$		0			0
$461$	32.4405	+	10.5406i	1.51091	+	0.490923i	0.943177	−	0.332291i	$-0.107822\pi$
$461$	32.4405	+	10.5406i	1.51091	+	0.490923i	0.567730	+	0.823215i	$0.307822\pi$
$462$		0			0
$463$	−39.9752	+	12.9887i	−1.85780	+	0.603637i	−0.862591	+	0.505902i	$0.831160\pi$
$463$	−39.9752	+	12.9887i	−1.85780	+	0.603637i	−0.995212	+	0.0977353i	$0.968840\pi$
$464$		0			0
$465$	−7.24250	−	25.8965i	−0.335863	−	1.20092i
$466$		0			0
$467$	−9.30036	+	6.75711i	−0.430370	+	0.312682i	−0.781797	−	0.623533i	$-0.785696\pi$
$467$	−9.30036	+	6.75711i	−0.430370	+	0.312682i	0.351427	+	0.936215i	$0.385696\pi$
$468$		0			0
$469$	2.70628	+	3.72488i	0.124964	+	0.171999i
$470$		0			0
$471$	24.6884	+	17.9372i	1.13758	+	0.826503i
$472$		0			0
$473$	2.87290	+	0.933461i	0.132096	+	0.0429206i
$474$		0			0
$475$	6.47091	+	2.71354i	0.296906	+	0.124506i
$476$		0			0
$477$	1.03729	−	3.19245i	0.0474942	−	0.146172i
$478$		0			0
$479$	−9.62460	−	6.99268i	−0.439759	−	0.319504i	0.345780	−	0.938316i	$-0.387614\pi$
$479$	−9.62460	−	6.99268i	−0.439759	−	0.319504i	−0.785539	+	0.618812i	$0.787614\pi$
$480$		0			0
$481$	−14.4158	+	10.4737i	−0.657302	+	0.477558i
$482$		0			0
$483$	2.48242	−	1.80359i	0.112954	−	0.0820660i
$484$		0			0
$485$	34.5726	+	12.8404i	1.56986	+	0.583053i
$486$		0			0
$487$	−20.8019	+	6.75894i	−0.942622	+	0.306277i	−0.739714	−	0.672921i	$-0.765039\pi$
$487$	−20.8019	+	6.75894i	−0.942622	+	0.306277i	−0.202908	+	0.979198i	$0.565039\pi$
$488$		0			0
$489$	−5.41477	+	16.6649i	−0.244864	+	0.753615i
$490$		0			0
$491$	3.07965	−	1.00064i	0.138983	−	0.0451582i	−0.238700	−	0.971093i	$-0.576721\pi$
$491$	3.07965	−	1.00064i	0.138983	−	0.0451582i	0.377682	+	0.925935i	$0.376721\pi$
$492$		0			0
$493$	22.6001			1.01786
$494$		0			0
$495$	4.28094	−	1.19725i	0.192414	−	0.0538126i
$496$		0			0
$497$	16.9019	−	23.2635i	0.758155	−	1.04351i
$498$		0			0
$499$			4.70824i			0.210770i	0.994432	+	0.105385i	$0.0336074\pi$
$499$			4.70824i			0.210770i	−0.994432	+	0.105385i	$0.966393\pi$
$500$		0			0
$501$		−	38.3961i		−	1.71541i
$502$		0			0
$503$	−7.58802	+	10.4440i	−0.338333	+	0.465676i	−0.943954	−	0.330078i	$-0.892925\pi$
$503$	−7.58802	+	10.4440i	−0.338333	+	0.465676i	0.605621	+	0.795754i	$0.292925\pi$
$504$		0			0
$505$	−41.9650	+	11.7364i	−1.86742	+	0.522262i
$506$		0			0
$507$	20.5969			0.914740
$508$		0			0
$509$	−8.87419	+	2.88340i	−0.393342	+	0.127804i	−0.499008	−	0.866597i	$-0.666302\pi$
$509$	−8.87419	+	2.88340i	−0.393342	+	0.127804i	0.105667	+	0.994402i	$0.466302\pi$
$510$		0			0
$511$	8.26534	−	25.4381i	0.365637	−	1.12532i
$512$		0			0
$513$	−17.7926	+	5.78117i	−0.785563	+	0.255245i
$514$		0			0
$515$	14.8157	+	5.50262i	0.652857	+	0.242474i
$516$		0			0
$517$	0.637117	−	0.462892i	0.0280204	−	0.0203580i
$518$		0			0
$519$	44.8777	−	32.6055i	1.96991	−	1.43122i
$520$		0			0
$521$	−14.6710	−	10.6591i	−0.642748	−	0.466984i	0.218045	−	0.975939i	$-0.430032\pi$
$521$	−14.6710	−	10.6591i	−0.642748	−	0.466984i	−0.860793	+	0.508955i	$0.830032\pi$
$522$		0			0
$523$	7.22455	−	22.2349i	0.315908	−	0.972264i	−0.659472	−	0.751729i	$-0.729220\pi$
$523$	7.22455	−	22.2349i	0.315908	−	0.972264i	0.975379	−	0.220534i	$-0.0707800\pi$
$524$		0			0
$525$	−3.93377	+	47.3365i	−0.171684	+	2.06594i
$526$		0			0
$527$	−18.3707	−	5.96899i	−0.800238	−	0.260013i
$528$		0			0
$529$	−18.5230	−	13.4577i	−0.805347	−	0.585119i
$530$		0			0
$531$	−22.5886	−	31.0905i	−0.980262	−	1.34921i
$532$		0			0
$533$	−22.8513	+	16.6025i	−0.989801	+	0.719132i
$534$		0			0
$535$	−6.77877	−	24.2384i	−0.293072	−	1.04792i
$536$		0			0
$537$	−64.5645	+	20.9783i	−2.78616	+	0.905279i
$538$		0			0
$539$	0.491627	+	0.159739i	0.0211759	+	0.00688046i
$540$		0			0
$541$	1.23623	−	0.401675i	0.0531496	−	0.0172694i	−0.282322	−	0.959320i	$-0.591104\pi$
$541$	1.23623	−	0.401675i	0.0531496	−	0.0172694i	0.335471	+	0.942050i	$0.391104\pi$
$542$		0			0
$543$		−	26.2128i		−	1.12490i
$544$		0			0
$545$	−11.8206	−	17.7747i	−0.506337	−	0.761384i
$546$		0			0
$547$	1.78489	+	1.29680i	0.0763163	+	0.0554470i	0.625289	−	0.780393i	$-0.284981\pi$
$547$	1.78489	+	1.29680i	0.0763163	+	0.0554470i	−0.548973	+	0.835840i	$0.684981\pi$
$548$		0			0
$549$			14.8256i			0.632739i
$550$		0			0
$551$	6.18915			0.263667
$552$		0			0
$553$	9.72359	−	13.3834i	0.413489	−	0.569119i
$554$		0			0
$555$	−28.7943	−	1.19438i	−1.22225	−	0.0506985i
$556$		0			0
$557$	22.2912			0.944509			0.472255	−	0.881462i	$-0.343440\pi$
$557$	22.2912			0.944509			0.472255	+	0.881462i	$0.343440\pi$
$558$		0			0
$559$	14.8679	+	45.7586i	0.628844	+	1.93538i
$560$		0			0
$561$	1.39910	−	4.30599i	0.0590701	−	0.181799i
$562$		0			0
$563$	6.54968	+	20.1578i	0.276036	+	0.849551i	0.988943	+	0.148293i	$0.0473780\pi$
$563$	6.54968	+	20.1578i	0.276036	+	0.849551i	−0.712907	+	0.701258i	$0.752622\pi$
$564$		0			0
$565$	−13.0858	−	19.6773i	−0.550526	−	0.827832i
$566$		0			0
$567$	−36.7469	−	50.5777i	−1.54322	−	2.12406i
$568$		0			0
$569$	1.34832	−	0.979610i	0.0565244	−	0.0410674i	−0.559164	−	0.829057i	$-0.688878\pi$
$569$	1.34832	−	0.979610i	0.0565244	−	0.0410674i	0.615689	+	0.787989i	$0.288878\pi$
$570$		0			0
$571$	−2.18726	+	3.01051i	−0.0915340	+	0.125986i	−0.852328	−	0.523008i	$-0.824810\pi$
$571$	−2.18726	+	3.01051i	−0.0915340	+	0.125986i	0.760794	+	0.648994i	$0.224810\pi$
$572$		0			0
$573$	3.49400	−	10.7534i	0.145964	−	0.449231i
$574$		0			0
$575$	−1.57199	+	0.370141i	−0.0655566	+	0.0154359i
$576$		0			0
$577$	−23.2030	−	7.53910i	−0.965952	−	0.313857i	−0.216771	−	0.976222i	$-0.569553\pi$
$577$	−23.2030	−	7.53910i	−0.965952	−	0.313857i	−0.749181	+	0.662366i	$0.769553\pi$
$578$		0			0
$579$	−25.1211	+	34.5763i	−1.04400	+	1.43694i
$580$		0			0
$581$	23.2438	+	31.9924i	0.964315	+	1.32727i
$582$		0			0
$583$	0.0761160	+	0.104765i	0.00315240	+	0.00433891i
$584$		0			0
$585$	55.5060	+	43.9544i	2.29489	+	1.81729i
$586$		0			0
$587$	4.25195	+	13.0862i	0.175497	+	0.540123i	0.999656	−	0.0262350i	$-0.00835183\pi$
$587$	4.25195	+	13.0862i	0.175497	+	0.540123i	−0.824159	+	0.566358i	$0.808352\pi$
$588$		0			0
$589$	−5.03089	−	1.63464i	−0.207294	−	0.0673540i
$590$		0			0
$591$	5.06187	+	15.5788i	0.208217	+	0.640827i
$592$		0			0
$593$			18.8934i			0.775861i	0.921689	+	0.387930i	$0.126810\pi$
$593$			18.8934i			0.775861i	−0.921689	+	0.387930i	$0.873190\pi$
$594$		0			0
$595$	26.7492	+	21.1823i	1.09661	+	0.868390i
$596$		0			0
$597$	32.4057	+	23.5441i	1.32628	+	0.963598i
$598$		0			0
$599$	−33.9391			−1.38671			−0.693356	−	0.720595i	$-0.743869\pi$
$599$	−33.9391			−1.38671			−0.693356	+	0.720595i	$0.743869\pi$
$600$		0			0
$601$	13.3568			0.544836			0.272418	−	0.962179i	$-0.412177\pi$
$601$	13.3568			0.544836			0.272418	+	0.962179i	$0.412177\pi$
$602$		0			0
$603$	8.97979	+	6.52420i	0.365685	+	0.265686i
$604$		0			0
$605$	8.50407	−	22.8970i	0.345740	−	0.930897i
$606$		0			0
$607$			22.7175i			0.922076i	0.887380	+	0.461038i	$0.152523\pi$
$607$			22.7175i			0.922076i	−0.887380	+	0.461038i	$0.847477\pi$
$608$		0			0
$609$	12.9468	+	39.8462i	0.524632	+	1.61465i
$610$		0			0
$611$	11.9294	+	3.87611i	0.482614	+	0.156811i
$612$		0			0
$613$	−9.25887	−	28.4959i	−0.373962	−	1.15094i	−0.944176	−	0.329441i	$-0.893140\pi$
$613$	−9.25887	−	28.4959i	−0.373962	−	1.15094i	0.570214	−	0.821496i	$-0.306860\pi$
$614$		0			0
$615$	−45.6437	−	1.89328i	−1.84053	−	0.0763445i
$616$		0			0
$617$	14.2585	+	19.6251i	0.574025	+	0.790077i	0.993024	−	0.117909i	$-0.0376192\pi$
$617$	14.2585	+	19.6251i	0.574025	+	0.790077i	−0.419000	+	0.907986i	$0.637619\pi$
$618$		0			0
$619$	−20.9345	−	28.8138i	−0.841428	−	1.15813i	−0.985687	−	0.168586i	$-0.946080\pi$
$619$	−20.9345	−	28.8138i	−0.841428	−	1.15813i	0.144259	−	0.989540i	$-0.453920\pi$
$620$		0			0
$621$	2.53092	−	3.48351i	0.101562	−	0.139788i
$622$		0			0
$623$	9.09160	+	2.95404i	0.364247	+	0.118351i
$624$		0			0
$625$	11.5441	−	22.1751i	0.461764	−	0.887003i
$626$		0			0
$627$	0.383150	−	1.17922i	0.0153016	−	0.0470933i
$628$		0			0
$629$	−12.1681	+	16.7480i	−0.485175	+	0.667786i
$630$		0			0
$631$	5.35186	−	3.88835i	0.213054	−	0.154793i	−0.476140	−	0.879369i	$-0.657965\pi$
$631$	5.35186	−	3.88835i	0.213054	−	0.154793i	0.689194	+	0.724576i	$0.257965\pi$
$632$		0			0
$633$	−14.2974	−	19.6786i	−0.568270	−	0.782156i
$634$		0			0
$635$	0.125778	−	3.03229i	0.00499135	−	0.120333i
$636$		0			0
$637$	2.54428	+	7.83048i	0.100808	+	0.310255i
$638$		0			0
$639$	21.4217	−	65.9293i	0.847430	−	2.60812i
$640$		0			0
$641$	6.78939	+	20.8956i	0.268165	+	0.825327i	0.990947	+	0.134251i	$0.0428629\pi$
$641$	6.78939	+	20.8956i	0.268165	+	0.825327i	−0.722782	+	0.691076i	$0.757137\pi$
$642$		0			0
$643$	−32.6614			−1.28804			−0.644019	−	0.765009i	$-0.722734\pi$
$643$	−32.6614			−1.28804			−0.644019	+	0.765009i	$0.722734\pi$
$644$		0			0
$645$	−27.0928	+	72.9469i	−1.06678	+	2.87228i
$646$		0			0
$647$	20.5295	−	28.2564i	0.807098	−	1.11088i	−0.184666	−	0.982801i	$-0.559120\pi$
$647$	20.5295	−	28.2564i	0.807098	−	1.11088i	0.991765	−	0.128074i	$-0.0408795\pi$
$648$		0			0
$649$	1.48256			0.0581954
$650$		0			0
$651$		−	35.8087i		−	1.40345i
$652$		0			0
$653$	−31.5991	−	22.9581i	−1.23657	−	0.898420i	−0.239204	−	0.970969i	$-0.576886\pi$
$653$	−31.5991	−	22.9581i	−1.23657	−	0.898420i	−0.997365	+	0.0725499i	$0.976886\pi$
$654$		0			0
$655$	1.11266	−	1.40508i	0.0434754	−	0.0549010i
$656$		0			0
$657$		−	64.4812i		−	2.51565i
$658$		0			0
$659$	−40.4722	+	13.1502i	−1.57657	+	0.512260i	−0.961171	−	0.275953i	$-0.911006\pi$
$659$	−40.4722	+	13.1502i	−1.57657	+	0.512260i	−0.615402	+	0.788213i	$0.711006\pi$
$660$		0			0
$661$	15.1858	+	4.93417i	0.590660	+	0.191917i	0.589071	−	0.808082i	$-0.299494\pi$
$661$	15.1858	+	4.93417i	0.590660	+	0.191917i	0.00158966	+	0.999999i	$0.499494\pi$
$662$		0			0
$663$	68.5844	−	22.2844i	2.66360	−	0.865455i
$664$		0			0
$665$	7.32538	+	5.80088i	0.284066	+	0.224948i
$666$		0			0
$667$	−1.15243	+	0.837290i	−0.0446223	+	0.0324200i
$668$		0			0
$669$	36.1792	+	49.7964i	1.39877	+	1.92524i
$670$		0			0
$671$	−0.462710	−	0.336178i	−0.0178627	−	0.0129780i
$672$		0			0
$673$	−8.44939	−	2.74537i	−0.325700	−	0.105826i	0.141603	−	0.989924i	$-0.454774\pi$
$673$	−8.44939	−	2.74537i	−0.325700	−	0.105826i	−0.467303	+	0.884097i	$0.654774\pi$
$674$		0			0
$675$	15.2768	+	64.8806i	0.588003	+	2.49726i
$676$		0			0
$677$	−7.28520	+	22.4216i	−0.279993	+	0.861730i	0.707862	+	0.706351i	$0.249660\pi$
$677$	−7.28520	+	22.4216i	−0.279993	+	0.861730i	−0.987855	+	0.155379i	$0.950340\pi$
$678$		0			0
$679$	39.7323	+	28.8672i	1.52478	+	1.10782i
$680$		0			0
$681$	62.1813	−	45.1773i	2.38279	−	1.73120i
$682$		0			0
$683$	20.8468	−	15.1461i	0.797680	−	0.579548i	−0.112553	−	0.993646i	$-0.535903\pi$
$683$	20.8468	−	15.1461i	0.797680	−	0.579548i	0.910233	+	0.414097i	$0.135903\pi$
$684$		0			0
$685$	−8.97503	−	13.4959i	−0.342918	−	0.515650i
$686$		0			0
$687$	−80.1042	+	26.0274i	−3.05617	+	0.993009i
$688$		0			0
$689$	−0.637371	+	1.96163i	−0.0242819	+	0.0747320i
$690$		0			0
$691$	28.3342	−	9.20634i	1.07788	−	0.350225i	0.284330	−	0.958726i	$-0.408229\pi$
$691$	28.3342	−	9.20634i	1.07788	−	0.350225i	0.793553	+	0.608501i	$0.208229\pi$
$692$		0			0
$693$	5.91952			0.224864
$694$		0			0
$695$	−0.0406647	+	0.980355i	−0.00154250	+	0.0371870i
$696$		0			0
$697$	−19.2885	+	26.5483i	−0.730602	+	1.00559i
$698$		0			0
$699$		−	77.1621i		−	2.91854i
$700$		0			0
$701$			5.84579i			0.220792i	0.993888	+	0.110396i	$0.0352120\pi$
$701$			5.84579i			0.220792i	−0.993888	+	0.110396i	$0.964788\pi$
$702$		0			0
$703$	−3.33230	+	4.58651i	−0.125680	+	0.172984i
$704$		0			0
$705$	11.2339	+	16.8925i	0.423092	+	0.636208i
$706$		0			0
$707$	−58.0275			−2.18235
$708$		0			0
$709$	18.5674	−	6.03290i	0.697312	−	0.226570i	0.0611529	−	0.998128i	$-0.480522\pi$
$709$	18.5674	−	6.03290i	0.697312	−	0.226570i	0.636159	+	0.771558i	$0.280522\pi$
$710$		0			0
$711$	12.3238	−	37.9288i	0.462179	−	1.42244i
$712$		0			0
$713$	1.15790	−	0.376224i	0.0433637	−	0.0140897i
$714$		0			0
$715$	−2.63046	+	0.735664i	−0.0983737	+	0.0275123i
$716$		0			0
$717$	39.7814	−	28.9028i	1.48566	−	1.07940i
$718$		0			0
$719$	−37.3747	+	27.1543i	−1.39384	+	1.01268i	−0.398408	+	0.917208i	$0.630437\pi$
$719$	−37.3747	+	27.1543i	−1.39384	+	1.01268i	−0.995432	+	0.0954761i	$0.969563\pi$
$720$		0			0
$721$	17.0268	+	12.3707i	0.634112	+	0.460709i
$722$		0			0
$723$	15.3836	−	47.3457i	0.572121	−	1.76081i
$724$		0			0
$725$	1.82620	−	21.9753i	0.0678232	−	0.816143i
$726$		0			0
$727$	−6.84600	−	2.22440i	−0.253904	−	0.0824984i	0.179300	−	0.983795i	$-0.442617\pi$
$727$	−6.84600	−	2.22440i	−0.253904	−	0.0824984i	−0.433204	+	0.901296i	$0.642617\pi$
$728$		0			0
$729$	−18.7064	−	13.5910i	−0.692831	−	0.503371i
$730$		0			0
$731$	32.8556	+	45.2219i	1.21521	+	1.67259i
$732$		0			0
$733$	−22.7156	+	16.5038i	−0.839018	+	0.609582i	−0.922096	−	0.386961i	$-0.873525\pi$
$733$	−22.7156	+	16.5038i	−0.839018	+	0.609582i	0.0830781	+	0.996543i	$0.473525\pi$
$734$		0			0
$735$	−4.63629	+	12.4831i	−0.171012	+	0.460446i
$736$		0			0
$737$	−0.407244	+	0.132322i	−0.0150010	+	0.00487413i
$738$		0			0
$739$	37.8363	+	12.2937i	1.39183	+	0.452233i	0.906540	−	0.422121i	$-0.138714\pi$
$739$	37.8363	+	12.2937i	1.39183	+	0.452233i	0.485290	+	0.874353i	$0.338714\pi$
$740$		0			0
$741$	18.7822	−	6.10270i	0.689980	−	0.224188i
$742$		0			0
$743$			20.8383i			0.764482i	0.924063	+	0.382241i	$0.124848\pi$
$743$			20.8383i			0.764482i	−0.924063	+	0.382241i	$0.875152\pi$
$744$		0			0
$745$	−3.56495	+	0.997013i	−0.130610	+	0.0365277i
$746$		0			0
$747$	77.1260	+	56.0353i	2.82189	+	2.05022i
$748$		0			0
$749$		−	33.5159i		−	1.22464i
$750$		0			0
$751$	48.8753			1.78348			0.891742	−	0.452545i	$-0.149484\pi$
$751$	48.8753			1.78348			0.891742	+	0.452545i	$0.149484\pi$
$752$		0			0
$753$	−4.86111	+	6.69075i	−0.177149	+	0.243824i
$754$		0			0
$755$	8.46943	+	30.2835i	0.308234	+	1.10213i
$756$		0			0
$757$	18.6251			0.676942			0.338471	−	0.940977i	$-0.390090\pi$
$757$	18.6251			0.676942			0.338471	+	0.940977i	$0.390090\pi$
$758$		0			0
$759$	0.0881851	+	0.271406i	0.00320092	+	0.00985141i
$760$		0			0
$761$	12.5520	−	38.6311i	0.455009	−	1.40037i	−0.416115	−	0.909312i	$-0.636609\pi$
$761$	12.5520	−	38.6311i	0.455009	−	1.40037i	0.871124	−	0.491063i	$-0.163391\pi$
$762$		0			0
$763$	−8.78414	−	27.0348i	−0.318007	−	0.978726i
$764$		0			0
$765$	77.1098	+	28.6390i	2.78791	+	1.03544i
$766$		0			0
$767$	13.8798	+	19.1039i	0.501169	+	0.689800i
$768$		0			0
$769$	14.8380	−	10.7804i	0.535072	−	0.388753i	−0.287179	−	0.957877i	$-0.592718\pi$
$769$	14.8380	−	10.7804i	0.535072	−	0.388753i	0.822252	+	0.569124i	$0.192718\pi$
$770$		0			0
$771$	3.73071	−	5.13489i	0.134358	−	0.184928i
$772$		0			0
$773$	10.0305	−	30.8706i	0.360770	−	1.11034i	−0.591817	−	0.806072i	$-0.701589\pi$
$773$	10.0305	−	30.8706i	0.360770	−	1.11034i	0.952588	−	0.304265i	$-0.0984107\pi$
$774$		0			0
$775$	−7.28841	+	17.3805i	−0.261807	+	0.624325i
$776$		0			0
$777$	−36.4990	−	11.8592i	−1.30939	−	0.425448i
$778$		0			0
$779$	−5.28223	+	7.27037i	−0.189256	+	0.260488i
$780$		0			0
$781$	1.57192	+	2.16357i	0.0562478	+	0.0774185i
$782$		0			0
$783$	34.5574	+	47.5641i	1.23498	+	1.69980i
$784$		0			0
$785$	−5.76068	−	20.5981i	−0.205607	−	0.735177i
$786$		0			0
$787$	−11.5801	−	35.6398i	−0.412785	−	1.27042i	−0.914217	−	0.405224i	$-0.867193\pi$
$787$	−11.5801	−	35.6398i	−0.412785	−	1.27042i	0.501432	−	0.865197i	$-0.332807\pi$
$788$		0			0
$789$	−47.2388	−	15.3488i	−1.68174	−	0.546432i
$790$		0			0
$791$	−9.72441	−	29.9287i	−0.345760	−	1.06414i
$792$		0			0
$793$		−	9.10969i		−	0.323495i
$794$		0			0
$795$	−2.77773	+	1.84725i	−0.0985159	+	0.0655152i
$796$		0			0
$797$	−44.1511	−	32.0777i	−1.56391	−	1.13625i	−0.932707	−	0.360636i	$-0.882560\pi$
$797$	−44.1511	−	32.0777i	−1.56391	−	1.13625i	−0.631207	−	0.775614i	$-0.717440\pi$
$798$		0			0
$799$	14.5727			0.515544
$800$		0			0
$801$	23.0456			0.814277
$802$		0			0
$803$	2.01248	+	1.46215i	0.0710187	+	0.0515981i
$804$		0			0
$805$	−2.14876	−	0.0891296i	−0.0757338	−	0.00314141i
$806$		0			0
$807$			4.21624i			0.148419i
$808$		0			0
$809$	−2.50898	−	7.72183i	−0.0882109	−	0.271485i	0.897214	−	0.441596i	$-0.145587\pi$
$809$	−2.50898	−	7.72183i	−0.0882109	−	0.271485i	−0.985425	+	0.170111i	$0.945587\pi$
$810$		0			0
$811$	1.71354	+	0.556763i	0.0601705	+	0.0195506i	0.338948	−	0.940805i	$-0.389929\pi$
$811$	1.71354	+	0.556763i	0.0601705	+	0.0195506i	−0.278777	+	0.960356i	$0.589929\pi$
$812$		0			0
$813$	14.2784	+	43.9445i	0.500766	+	1.54120i
$814$		0			0
$815$	10.2263	−	6.80073i	0.358213	−	0.238219i
$816$		0			0
$817$	8.99767	+	12.3842i	0.314789	+	0.433269i
$818$		0			0
$819$	55.4188	+	76.2775i	1.93649	+	2.66535i
$820$		0			0
$821$	13.9783	−	19.2395i	0.487848	−	0.671465i	−0.492142	−	0.870515i	$-0.663786\pi$
$821$	13.9783	−	19.2395i	0.487848	−	0.671465i	0.979989	+	0.199051i	$0.0637858\pi$
$822$		0			0
$823$	22.5499	+	7.32692i	0.786042	+	0.255400i	0.674418	−	0.738350i	$-0.264395\pi$
$823$	22.5499	+	7.32692i	0.786042	+	0.255400i	0.111624	+	0.993751i	$0.464395\pi$
$824$		0			0
$825$	−4.07389	−	1.70837i	−0.141835	−	0.0594777i
$826$		0			0
$827$	−2.73313	+	8.41171i	−0.0950402	+	0.292504i	−0.987264	−	0.159089i	$-0.949144\pi$
$827$	−2.73313	+	8.41171i	−0.0950402	+	0.292504i	0.892224	+	0.451593i	$0.149144\pi$
$828$		0			0
$829$	−4.69015	+	6.45543i	−0.162896	+	0.224206i	−0.882660	−	0.470012i	$-0.844250\pi$
$829$	−4.69015	+	6.45543i	−0.162896	+	0.224206i	0.719765	+	0.694218i	$0.244250\pi$
$830$		0			0
$831$	33.0413	−	24.0059i	1.14619	−	0.832755i
$832$		0			0
$833$	5.62245	+	7.73864i	0.194806	+	0.268128i
$834$		0			0
$835$	−16.7066	+	21.0972i	−0.578156	+	0.730100i
$836$		0			0
$837$	−15.5279	−	47.7898i	−0.536721	−	1.65186i
$838$		0			0
$839$	14.2160	−	43.7523i	0.490790	−	1.51050i	−0.332627	−	0.943058i	$-0.607935\pi$
$839$	14.2160	−	43.7523i	0.490790	−	1.51050i	0.823417	−	0.567437i	$-0.192065\pi$
$840$		0			0
$841$	2.95111	+	9.08258i	0.101762	+	0.313193i
$842$		0			0
$843$	10.0497			0.346130
$844$		0			0
$845$	−11.3172	−	8.96196i	−0.389324	−	0.308301i
$846$		0			0
$847$	19.1184	−	26.3142i	0.656917	−	0.904168i
$848$		0			0
$849$	40.2003			1.37967
$850$		0			0
$851$		−	1.30482i		−	0.0447287i
$852$		0			0
$853$	37.0549	+	26.9220i	1.26874	+	0.921790i	0.999151	−	0.0411867i	$-0.0131138\pi$
$853$	37.0549	+	26.9220i	1.26874	+	0.921790i	0.269584	+	0.962977i	$0.413114\pi$
$854$		0			0
$855$	21.1169	+	7.84292i	0.722182	+	0.268222i
$856$		0			0
$857$		−	46.7189i		−	1.59589i	−0.602733	−	0.797943i	$-0.705922\pi$
$857$		−	46.7189i		−	1.59589i	0.602733	−	0.797943i	$-0.294078\pi$
$858$		0			0
$859$	−35.3436	+	11.4838i	−1.20591	+	0.391824i	−0.841932	−	0.539584i	$-0.818582\pi$
$859$	−35.3436	+	11.4838i	−1.20591	+	0.391824i	−0.363978	+	0.931408i	$0.618582\pi$
$860$		0			0
$861$	−57.8569	−	18.7988i	−1.97176	−	0.640662i
$862$		0			0
$863$	−47.5068	+	15.4359i	−1.61715	+	0.525444i	−0.971267	−	0.237992i	$-0.923511\pi$
$863$	−47.5068	+	15.4359i	−1.61715	+	0.525444i	−0.645883	+	0.763436i	$0.723511\pi$
$864$		0			0
$865$	−38.8457	−	1.61130i	−1.32079	−	0.0547859i
$866$		0			0
$867$	23.9019	−	17.3657i	0.811750	−	0.589771i
$868$		0			0
$869$	0.904318	+	1.24469i	0.0306769	+	0.0422231i
$870$		0			0
$871$	−5.51771	−	4.00885i	−0.186960	−	0.135835i
$872$		0			0
$873$	112.602	+	36.5866i	3.81100	+	1.23827i
$874$		0			0
$875$	22.7582	−	24.2980i	0.769366	−	0.821423i
$876$		0			0
$877$	−8.12444	+	25.0044i	−0.274343	+	0.844340i	0.715050	+	0.699073i	$0.246404\pi$
$877$	−8.12444	+	25.0044i	−0.274343	+	0.844340i	−0.989393	+	0.145267i	$0.953596\pi$
$878$		0			0
$879$	−23.7381	−	17.2467i	−0.800666	−	0.581718i
$880$		0			0
$881$	−13.3185	+	9.67642i	−0.448710	+	0.326007i	−0.789086	−	0.614282i	$-0.789446\pi$
$881$	−13.3185	+	9.67642i	−0.448710	+	0.326007i	0.340376	+	0.940289i	$0.389446\pi$
$882$		0			0
$883$	5.10972	−	3.71243i	0.171956	−	0.124933i	−0.498479	−	0.866902i	$-0.666108\pi$
$883$	5.10972	−	3.71243i	0.171956	−	0.124933i	0.670434	+	0.741969i	$0.266108\pi$
$884$		0			0
$885$	−1.58280	+	38.1585i	−0.0532051	+	1.28268i
$886$		0			0
$887$	26.2498	−	8.52907i	0.881381	−	0.286378i	0.166850	−	0.985982i	$-0.446640\pi$
$887$	26.2498	−	8.52907i	0.881381	−	0.286378i	0.714531	+	0.699604i	$0.246640\pi$
$888$		0			0
$889$	1.24888	−	3.84365i	0.0418860	−	0.128912i
$890$		0			0
$891$	5.52971	−	1.79671i	0.185252	−	0.0601922i
$892$		0			0
$893$	3.99079			0.133547
$894$		0			0
$895$	44.6036	+	16.5660i	1.49094	+	0.553741i
$896$		0			0
$897$	−2.67168	+	3.67725i	−0.0892047	+	0.122780i
$898$		0			0
$899$			16.6237i			0.554431i
$900$		0			0
$901$			2.39626i			0.0798312i
$902$		0			0
$903$	−60.9087	+	83.8337i	−2.02692	+	2.78981i
$904$		0			0
$905$	−11.4055	+	14.4030i	−0.379132	+	0.478771i
$906$		0			0
$907$	15.5893			0.517636			0.258818	−	0.965926i	$-0.416667\pi$
$907$	15.5893			0.517636			0.258818	+	0.965926i	$0.416667\pi$
$908$		0			0
$909$	−133.044	+	43.2286i	−4.41279	+	1.43380i
$910$		0			0
$911$	−8.96903	+	27.6038i	−0.297157	+	0.914556i	0.685331	+	0.728232i	$0.259658\pi$
$911$	−8.96903	+	27.6038i	−0.297157	+	0.914556i	−0.982488	+	0.186324i	$0.940342\pi$
$912$		0			0
$913$	−3.49776	+	1.13649i	−0.115759	+	0.0376123i
$914$		0			0
$915$	9.14666	−	11.5505i	0.302379	−	0.381846i
$916$		0			0
$917$	1.93089	−	1.40287i	0.0637636	−	0.0463270i
$918$		0			0
$919$	−34.5740	+	25.1195i	−1.14049	+	0.828616i	−0.987188	−	0.159563i	$-0.948991\pi$
$919$	−34.5740	+	25.1195i	−1.14049	+	0.828616i	−0.153304	+	0.988179i	$0.548991\pi$
$920$		0			0
$921$	−62.9005	−	45.6999i	−2.07264	−	1.50586i
$922$		0			0
$923$	−13.1628	+	40.5108i	−0.433258	+	1.33343i
$924$		0			0
$925$	15.3017	+	13.1850i	0.503118	+	0.433521i
$926$		0			0
$927$	48.2544	+	15.6788i	1.58488	+	0.514959i
$928$		0			0
$929$	−7.83492	−	5.69240i	−0.257055	−	0.186762i	0.451792	−	0.892123i	$-0.350785\pi$
$929$	−7.83492	−	5.69240i	−0.257055	−	0.186762i	−0.708848	+	0.705361i	$0.750785\pi$
$930$		0			0
$931$	1.53974	+	2.11926i	0.0504628	+	0.0694561i
$932$		0			0
$933$	64.7208	−	47.0224i	2.11886	−	1.53945i
$934$		0			0
$935$	−2.64234	+	1.75721i	−0.0864138	+	0.0574670i
$936$		0			0
$937$	45.0827	−	14.6482i	1.47279	−	0.478537i	0.540837	−	0.841127i	$-0.318107\pi$
$937$	45.0827	−	14.6482i	1.47279	−	0.478537i	0.931949	+	0.362590i	$0.118107\pi$
$938$		0			0
$939$	−33.1045	−	10.7563i	−1.08032	−	0.351018i
$940$		0			0
$941$	−14.2417	+	4.62742i	−0.464267	+	0.150850i	−0.531804	−	0.846867i	$-0.678486\pi$
$941$	−14.2417	+	4.62742i	−0.464267	+	0.150850i	0.0675373	+	0.997717i	$0.478486\pi$
$942$		0			0
$943$		−	2.06835i		−	0.0673549i
$944$		0			0
$945$	−3.67864	+	88.6855i	−0.119666	+	2.88494i
$946$		0			0
$947$	−21.2273	−	15.4226i	−0.689796	−	0.501166i	0.186797	−	0.982398i	$-0.440189\pi$
$947$	−21.2273	−	15.4226i	−0.689796	−	0.501166i	−0.876593	+	0.481233i	$0.840189\pi$
$948$		0			0
$949$			39.6210i			1.28615i
$950$		0			0
$951$	−2.74274			−0.0889394
$952$		0			0
$953$	−17.5587	+	24.1675i	−0.568782	+	0.782861i	−0.992410	−	0.122975i	$-0.960756\pi$
$953$	−17.5587	+	24.1675i	−0.568782	+	0.782861i	0.423628	+	0.905836i	$0.360756\pi$
$954$		0			0
$955$	−6.59877	+	4.38832i	−0.213531	+	0.142003i
$956$		0			0
$957$	−3.89651			−0.125956
$958$		0			0
$959$	−6.66957	−	20.5268i	−0.215371	−	0.662845i
$960$		0			0
$961$	−5.18900	+	15.9701i	−0.167387	+	0.515164i
$962$		0			0
$963$	−24.9682	−	76.8443i	−0.804590	−	2.47627i
$964$		0			0
$965$	28.8477	−	8.06786i	0.928640	−	0.259713i
$966$		0			0
$967$	−15.3115	−	21.0745i	−0.492385	−	0.677710i	0.488440	−	0.872597i	$-0.337566\pi$
$967$	−15.3115	−	21.0745i	−0.492385	−	0.677710i	−0.980826	+	0.194887i	$0.937566\pi$
$968$		0			0
$969$	18.5619	−	13.4860i	0.596294	−	0.433233i
$970$		0			0
$971$	−1.38452	+	1.90563i	−0.0444314	+	0.0611546i	−0.830655	−	0.556788i	$-0.812034\pi$
$971$	−1.38452	+	1.90563i	−0.0444314	+	0.0611546i	0.786223	+	0.617943i	$0.212034\pi$
$972$		0			0
$973$	−0.403769	+	1.24267i	−0.0129442	+	0.0398383i
$974$		0			0
$975$	−16.1264	−	68.4890i	−0.516458	−	2.19340i
$976$		0			0
$977$	−8.92406	−	2.89960i	−0.285506	−	0.0927665i	0.162763	−	0.986665i	$-0.447959\pi$
$977$	−8.92406	−	2.89960i	−0.285506	−	0.0927665i	−0.448269	+	0.893899i	$0.647959\pi$
$978$		0			0
$979$	−0.522574	+	0.719261i	−0.0167015	+	0.0229877i
$980$		0			0
$981$	−40.2801	−	55.4407i	−1.28604	−	1.77009i
$982$		0			0
$983$	−32.0991	−	44.1807i	−1.02380	−	1.40914i	−0.909503	−	0.415698i	$-0.863537\pi$
$983$	−32.0991	−	44.1807i	−1.02380	−	1.40914i	−0.114301	−	0.993446i	$-0.536463\pi$
$984$		0			0
$985$	3.99723	−	10.7625i	0.127362	−	0.342920i
$986$		0			0
$987$	8.34816	+	25.6930i	0.265725	+	0.817817i
$988$		0			0
$989$	−3.35076	−	1.08873i	−0.106548	−	0.0346196i
$990$		0			0
$991$	−19.1415	−	58.9116i	−0.608051	−	1.87139i	−0.474273	−	0.880378i	$-0.657289\pi$
$991$	−19.1415	−	58.9116i	−0.608051	−	1.87139i	−0.133778	−	0.991011i	$-0.542711\pi$
$992$		0			0
$993$			27.0472i			0.858316i
$994$		0			0
$995$	−7.56139	−	27.0368i	−0.239712	−	0.857123i
$996$		0			0
$997$	24.8911	+	18.0845i	0.788310	+	0.572741i	0.907462	−	0.420135i	$-0.138017\pi$
$997$	24.8911	+	18.0845i	0.788310	+	0.572741i	−0.119151	+	0.992876i	$0.538017\pi$
$998$		0			0
$999$	−53.8537			−1.70386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.be.a.529.1		112
4.3	odd	2		200.2.o.a.29.7	✓	112
8.3	odd	2		200.2.o.a.29.13	yes	112
8.5	even	2	inner	800.2.be.a.529.28		112
20.3	even	4		1000.2.t.b.101.40		224
20.7	even	4		1000.2.t.b.101.17		224
20.19	odd	2		1000.2.o.a.149.22		112
25.19	even	10	inner	800.2.be.a.369.28		112
40.3	even	4		1000.2.t.b.101.6		224
40.19	odd	2		1000.2.o.a.149.16		112
40.27	even	4		1000.2.t.b.101.51		224
100.19	odd	10		200.2.o.a.69.13	yes	112
100.31	odd	10		1000.2.o.a.349.16		112
100.67	even	20		1000.2.t.b.901.51		224
100.83	even	20		1000.2.t.b.901.6		224
200.19	odd	10		200.2.o.a.69.7	yes	112
200.67	even	20		1000.2.t.b.901.17		224
200.69	even	10	inner	800.2.be.a.369.1		112
200.83	even	20		1000.2.t.b.901.40		224
200.131	odd	10		1000.2.o.a.349.22		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.7	✓	112	4.3	odd	2
200.2.o.a.29.13	yes	112	8.3	odd	2
200.2.o.a.69.7	yes	112	200.19	odd	10
200.2.o.a.69.13	yes	112	100.19	odd	10
800.2.be.a.369.1		112	200.69	even	10	inner
800.2.be.a.369.28		112	25.19	even	10	inner
800.2.be.a.529.1		112	1.1	even	1	trivial
800.2.be.a.529.28		112	8.5	even	2	inner
1000.2.o.a.149.16		112	40.19	odd	2
1000.2.o.a.149.22		112	20.19	odd	2
1000.2.o.a.349.16		112	100.31	odd	10
1000.2.o.a.349.22		112	200.131	odd	10
1000.2.t.b.101.6		224	40.3	even	4
1000.2.t.b.101.17		224	20.7	even	4
1000.2.t.b.101.40		224	20.3	even	4
1000.2.t.b.101.51		224	40.27	even	4
1000.2.t.b.901.6		224	100.83	even	20
1000.2.t.b.901.17		224	200.67	even	20
1000.2.t.b.901.40		224	200.83	even	20
1000.2.t.b.901.51		224	100.67	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.be (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.58107 - 1.87526i) q^{3} +(0.602254 + 2.15344i) q^{5} +2.97769i q^{7} +(2.21828 + 6.82716i) q^{9} +O(q^{10})\)	\(q+(-2.58107 - 1.87526i) q^{3} +(0.602254 + 2.15344i) q^{5} +2.97769i q^{7} +(2.21828 + 6.82716i) q^{9} +(-0.263378 - 0.0855768i) q^{11} +(-1.36304 - 4.19500i) q^{13} +(2.48379 - 6.68755i) q^{15} +(-3.01210 - 4.14580i) q^{17} +(-0.824879 - 1.13535i) q^{19} +(5.58392 - 7.68561i) q^{21} +(0.307187 + 0.0998113i) q^{23} +(-4.27458 + 2.59383i) q^{25} +(4.11950 - 12.6785i) q^{27} +(-2.59226 + 3.56794i) q^{29} +(3.04947 - 2.21557i) q^{31} +(0.519319 + 0.714781i) q^{33} +(-6.41226 + 1.79332i) q^{35} +(-1.24835 - 3.84202i) q^{37} +(-4.34861 + 13.3836i) q^{39} +(-1.97884 - 6.09023i) q^{41} -10.9079 q^{43} +(-13.3659 + 8.88860i) q^{45} +(-1.67150 + 2.30062i) q^{47} -1.86662 q^{49} +16.3491i q^{51} +(-0.378304 - 0.274854i) q^{53} +(0.0256637 - 0.618708i) q^{55} +4.47727i q^{57} +(-5.09147 + 1.65432i) q^{59} +(1.96419 + 0.638204i) q^{61} +(-20.3291 + 6.60534i) q^{63} +(8.21278 - 5.46168i) q^{65} +(1.25093 - 0.908853i) q^{67} +(-0.605700 - 0.833675i) q^{69} +(-7.81261 - 5.67620i) q^{71} +(-8.54291 - 2.77576i) q^{73} +(15.8971 + 1.32108i) q^{75} +(0.254821 - 0.784258i) q^{77} +(-4.49455 - 3.26548i) q^{79} +(-16.9856 + 12.3407i) q^{81} +(10.7440 - 7.80599i) q^{83} +(7.11368 - 8.98320i) q^{85} +(13.3816 - 4.34795i) q^{87} +(0.992059 - 3.05324i) q^{89} +(12.4914 - 4.05871i) q^{91} -12.0257 q^{93} +(1.94811 - 2.46009i) q^{95} +(9.69449 - 13.3433i) q^{97} -1.98796i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 30 q^{9}+O(q^{10}) \) 112 * q - 30 * q^9	\( 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79} - 6 q^{81} + 10 q^{87} + 24 q^{89} + 86 q^{95} - 50 q^{97}+O(q^{100}) \) 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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